There are viewpoints expressed that chivalry should be redefined as common courtesy and that it should be extended to everyone of either gender. Of course we want to encourage politeness and courtesy to everyone (certainly our society can do with more of that). However, eliminating the concept of chivalry in an attempt to fit into a bland same thing for everyone approach minimizes the value that it can have in the dealings between women and men. It's as if in an effort to modernize, everything from the past is supposed to be discarded.
Between these messages that it's outdated and should just be forgotten and those messages expressing that there is something wrong with its traditional application of men's courteous and respectful behavior toward women, it's been tough for chivalry to bounce back off the deck. Chivalry took a beating (and to many people became "dead" in the late 1960s and early 1970s when it got hijacked. A warning message took hold that chivalry really meant that women were somehow an inferior gender and that the hidden meaning was about men displaying their dominance. Some of that came from a need to ensure a bit more of a radical message so that it would attract attention and invite controversy as the women's movement was justifiably looking to make strides.
Yet it also came at a time when the movement for equality became conflated with a need for sameness, as if men and women had to be exactly the same if they were to be equal. In more recent times, we've thankfully moved past such a rigid approach that equality has be mean sameness. It's not unusual for women to speak of unique ways to sell to women as opposed to selling to men, recognizing that we do indeed think differently. It's common in women's groups to hear discussions of the difference in communication styles and bonding between women as opposed to that of men. It's known that chemical reactions to stress or hunger differ in how they impact each gender, so our needs and responses differ. There are different roles, and accepting that does not mean that either gender is superior, or that it somehow implies there shouldn't be equal opportunity for both men and women to achieve their potential. Of course there should.
But given all that, it also is striking how many women express the yearning to see chivalry displayed. To accept that men and women have some places where our roles aren't somehow unisex. That doesn't mean every last woman feels this way, and some continue to look at it with the meaning of subservience that took hold during the tumultuous 60s-70s. And some men are there who still express resentment about women still looking for it as if the achievement of some strides in the 60s, 70s and the years since meant that women had forfeited their "right" to receive such treatment.
Of course no woman should be forced to accept chivalry if her beliefs are that doing so undermines her independence; yet I would encourage those women to take the offering of chivalry as a gesture of politeness they are free to politely decline. (A recent survey about chivalry showed that a large majority of women appreciate the gesture, with only 7% feeling it is patronizing.)
In fact, the men who do practice it should be grateful that not every man does it. It provides a wonderful tool to catch a woman's eye in the first place, or to help her appreciate the relationship she's in a little more than all the others.
It is not simply the same as general politeness and courtesy in that it's offered by men as a gesture offered for women to accept. It held that stature in the past, and now that society has allowed men and women to accept (and respect) we have some innate differences, it can be that way again.